GCSE · Basic probability

Sample space & systematic listingExam-style questions

How to list every outcome once and only once — systematic listing, two-way sample-space diagrams, the product rule for counting, and why swapping two things over sometimes makes a new outcome and sometimes doesn't.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Two fair six-sided dice are rolled and the two scores are added to give a total.

(a) Find the probability that the total is $5$ .

(b) Find the probability that the total is at least $10$ .

(c) Jay says: "The total can be any whole number from $2$ to $12$ , so there are $11$ possible outcomes and the probability of a total of $5$ is $\frac{1}{11}$ ."

Explain why Jay is wrong.
Level 3 · 5 marksTry it
2
Two fair six-sided dice are rolled. The score is the positive difference between the two numbers rolled. For example, a $6$ and a $2$ give a score of $4$ , and a $3$ and a $3$ give a score of $0$ .

(a) Find the probability that the score is $1$ .

(b) Find the probability that the score is $3$ or more.

(c) Write down the most likely score, and explain how the sample space shows this.
Level 3 · 6 marksTry it